arXiv Analytics

Sign in

arXiv:math/0512339 [math.CO]AbstractReferencesReviewsResources

Sortable elements and Cambrian lattices

Nathan Reading

Published 2005-12-14Version 1

We show that the Coxeter-sortable elements in a finite Coxeter group W are the minimal congruence-class representatives of a lattice congruence of the weak order on W. We identify this congruence as the Cambrian congruence on W, so that the Cambrian lattice is the weak order on Coxeter-sortable elements. These results exhibit W-Catalan combinatorics arising in the context of the lattice theory of the weak order on W.

Comments: 23 pages, 9 figures
Categories: math.CO
Subjects: 20F55, 06B10
Related articles: Most relevant | Search more
arXiv:math/0401404 [math.CO] (Published 2004-01-28)
Lattice congruences of the weak order
arXiv:math/0402086 [math.CO] (Published 2004-02-05, updated 2005-07-18)
Cambrian Lattices
arXiv:2309.14261 [math.CO] (Published 2023-09-25)
The $s$-weak order and $s$-permutahedra II: The combinatorial complex of pure intervals

Links

Toolbox